Support Accept Reject Abstain voting
Support Accept Reject Abstain (SARA) voting is very similar to Majority Acceptable Score voting, which is the graded Bucklin method which uses 3 grade levels and breaks median ties using Score voting. SARA works as follows:
 Voters can support, accept, reject, or abstain on each candidate. These are worth 2, 1, 0, and 0 points, respectively. Default is abstain.
 Eliminate all candidates rejected by over 50%, and any who average under half a point per voter, unless that would eliminate all of them.
 Highest points wins. In case of a tie, fewest rejections wins.
As the first round of a tworound system ("SARA with runoff")
If this system is used as the first round of a tworound runoff, then you want to use it to elect at two finalists in the first round. Thus, run the system twice. The first time, replace "50%" in step 2 with "2/3".
Then, to find the second winner, if the firsttime winner got 1/3 or more support, first downweight those ballots as if you'd eliminated enough of them to make up 1/3 of the electorate. Otherwise, discard all of the ballots which supported firsttime winner. After downweighting or discarding, run MAS normally.
If all the candidates in the first round got a majority of 0's, then you can still find two finalists as explained above. But the voters have sent a message that none of the candidates are good, so one way to deal with the situation would be to have a rule to allow candidates to transfer their 2votes to new candidates who were not running in the first round, and if those transfers would have made the new candidates finalists, then add them to the second round along with the two finalists who did best in the first round. In that case, since there would be more than 2 candidates in the second round, it would be important to use MAS for the second round too.
Relationship to NOTA
As discussed in the above section, if all the candidates in the first round got a majority "reject", then the voters have sent a message that none of the candidates are good, akin to a result of "none of the above" (NOTA). MAS still gives a winner, but it might be good to have a rule that such a winner could only serve one term, or perhaps a softer rule that if they run for the same office again, the information of what percent of voters rejected them should be next to their name on the ballot
An example
Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities, and that everyone wants to live as near the capital as possible.
The candidates for the capital are:
 Memphis, the state's largest city, with 42% of the voters, but located far from the other cities
 Nashville, with 26% of the voters, near the center of Tennessee
 Knoxville, with 17% of the voters
 Chattanooga, with 15% of the voters
The preferences of the voters would be divided like this:
42% of voters (close to Memphis) 
26% of voters (close to Nashville) 
15% of voters (close to Chattanooga) 
17% of voters (close to Knoxville) 





Assume voters in each city give their own city 2; any city within 100 miles, 1; any city between 100 and 200 miles, a blank; and any city that is over 200 miles away or is the farthest city, 0. (These assumptions can be varied substantially without changing the result, but they seem reasonable to start with.)
City  Support  Accept  Reject <50 
Abstain  score >50 

Memphis  42  0  58  0  (84) 
Nashville  26  0  0  74  52 
Chattanooga  15  17  42  26  47 
Knoxville  17  15  42  26  49 
Memphis is explicitly given 0 by a majority, and is eliminated. Chattanooga and Knoxville are both given 0 by a majority implicitly, so they are eliminated. Nashville remains and wins.
If Memphis voters tried to strategize by rating Nashville at 0 in the above scenario, Chattanooga and Knoxville voters could protect against this strategy if 2/3 of them gave Nashville a 1.